Maths

### Graph the solution sets of the following inequations:

Given $x+2 y>1$ $\begin{array}{l} \Rightarrow 2 y>1-x \\ \Rightarrow y>\frac{1}{2}-\frac{x}{2} \end{array}$ Consider the equation $y=\frac{1}{2}-\frac{x}{2}$ Finding points on the...

### A manufacturer produces two Models of bikes – Model and Model . Model takes 6 man-hours to make per unit, while Model Y takes 10 man-hours per unit. There is a total of 450 man-hour available per week. Handling and Marketing costs are Rs 2000 and Rs 1000 per unit for Models and respectively. The total funds available for these purposes are Rs 80,000 per week. Profits per unit for Models and are Rs 1000 and Rs 500 , respectively. How many bikes of each model should the manufacturer produce so as to yield a maximum profit? Find the maximum profit.

Solution: Let us take $\mathrm{x}$ an $\mathrm{y}$ to be the no. of models of bike produced by the manufacturer. From the question we have, Model $x$ takes 6 man-hours to make per unit Model $y$...

### In Fig. 12.11, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of

Solution: It is seen from the given figure, that the corner points are as follows: $\mathrm{R}(7 / 2,3 / 4), \mathrm{Q}(3 / 2,15 / 4), \mathrm{P}(3 / 13,24 / 13)$ and $\mathrm{S}(18 / 7,2 / 7)$ On...

### Minimize subject to the constraints: .

Solution: It is given that: $\mathrm{Z}=13 \mathrm{x}-15 \mathrm{y}$ and the constraints $\mathrm{x}+\mathrm{y} \leq 7$, $2 x-3 y+6 \geq 0, x \geq 0, y \geq 0$ Taking $x+y=7$, we have...

### Find the solution of : dy/dx = 2^y-x

ACCORDING TO QUES,

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### Find inverse, by elementary row operations (if possible), of the following matrices

Ans: Since, we obtain all the zeroes in a row of the matrix A, L.H.S., A-1 does not exist.

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### If and x2 = –1, then show that (A + B)2 = A2 + B2

Answer: According to the given ques

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### Let and a = 4, b = –2. Show that: (A – B)T = AT – BT

Answer: According to the given ques,

### Let and a = 4, b = –2. Show that: (a) (AB)T = BT AT (b) (A –B)C = AC – BC

Answer: According to the given ques, (a) (b)

### Let and a = 4, b = –2. Show that: (a) (AT)T = A (b) (bA)T = b AT

Answer: According to the given ques

### Let and a = 4, b = –2. Show that: (a) A + (B + C) = (A + B) + C (b) A (BC) = (AB) C

Answer: According to the given ques